Meta-heuristic Algorithms for Nesting Problem of Rectangular Pieces

Nesting problems consist of placing multiple items onto larger shapes finding a good arrangement. The goal of the nesting process is to minimize the waste of material. It is common to assume, as in the present work, that the stock sheet has fixed width and infinite height, since in the real world a company may have to cut pieces from a roll of material. The complexity of such problems is often faced with a two-stage approach, so-called \u201chybrid algorithm\u201d, combining a placement routine and a meta-heuristic algorithm. Starting from a given positioning sequence, the placement routine generates a non-overlapping configuration. The encoded solution is manipulated and modified by the meta-heuristic algorithm to generate a new sequence that brings to a better value of the objective function (in this case the height of the strip). The proposed method consists in placing the rectangles inside a strip and in combining the meta-heuristic algorithms with the No Fit Polygon algorithm. The software has been developed in Python language using proper libraries to solve the meta-heuristic techniques (Inspyred) and the geometric problems (Polygon). The results show the effectiveness of the proposed method; moreover, with regard to problems reported in literature employed as benchmark of the nesting algorithms, the degree of occupation values (Efficiency Ratio, ER) are shown to be higher than 90%

Low\u2010cost, High\u2010Capability, Embedded Systems for CNC Education and Research

Teaching of CNC and CAD/CAM technologies has recently taken a great importance, due to their development, to the great number of solutions available on the market, and to the frequent updates. Nevertheless, one of the most urgent need is to improve the quality of education coping with a rapidly growing number of students. Nowadays, in comparison to the past, many Open-Source technical solutions, both hardware and software, are available to realise easily and cheaply some scaled-down prototypes of numerical control machine tools: these are able to work perfectly and can be employed as a learning method. This paper shows some past experiences regarding the development of some degree thesis works. In particular, it is shown how to implement a numerical control (LinuxCNC) in two specific cheap embedded systems (Raspberry Pi and BeagleBone Black). In this way, a student has the possibility of simulating the working of a complete Numerical Control and of learning interactively its way of programming. The final result and student response have shown an excellent effectiveness of these experiences and easy to use as powerful tool in engineering education

Optimal positioning of irregular shapes in stamping die strip

The nesting of two-dimensional shapes is a common problem, where raw material has to be economically cut. As for the single-pass single-row strip layout, several algorithms, based on established methods, have been proposed. Moreover, it should be noticed that the optimum layout should also consider a few constraints, like grain orientation for subsequent forming operation, correct bridge width, and the commercial roll of metal width in order to make solutions applicable in real industrial environments. Most of the procedures until now shown in literature are quite complex and often ignore these real constraints. They usually make use of sliding techniques and are not able to effectively work with relatively multiple-connected figures. In particular, most of the different proposed procedures are based on the No Fit Polygon (NFP) computation of non-convex polygons, which often generates holes. This work is a proposal for a more efficient method, which can be used in heuristic procedures. In order to overcome some faults of most of the former methods presented in literature, in this paper a new geometric entity called \u201cNo Fit Path\u201d (NFPh) of non-convex polygons is applied. It allows researchers to find solutions of nesting problems even when there are NFP faults due to degenerate solutions. Moreover, the No Fit Path allows researchers to easily read, modify, or share their results, overcoming all those problems arising from the usual large amount of information and from the different origins and formats of the obtained data. Given two non-convex polygons, the algorithm is able to calculate their NFPh very quickly and without any approximation by a polygon clipping method. In this paper a totally automated procedure has been developed. This procedure firstly obtains the \u201cNo Fit Path\u201d (NFPh); secondly, between all the existing positions on the NFPh, the algorithm searches the optimal one, minimizing the global waste. The proposed approach also allows designers to set an optimal orientation of the shapes on the roll of metal, taking account of the grain orientation in order to obtain the best mechanical characteristics for the cut pieces

A numerical approach for the modelling of forming limits in hot incremental forming of AZ31 magnesium alloy

Magnesium alloys, because of their good specific material strength, can be considered attractive by different industry fields, as the aerospace and the automotive one. However, their use is limited by the poor formability at room temperature. In this research, a numerical approach is proposed in order to determine an analytical expression of material formability in hot incremental forming processes. The numerical model was developed using the commercial software ABAQUS/Explicit. The Johnson-Cook material model was used, and the model was validated through experimental measurements carried out using the ARAMIS system. Different geometries were considered with temperature varying in a range of 25–400 °C and wall angle in a range of 35–60°. An analytical expression of the fracture forming limit, as a function of temperature, was established and finally tested with a different geometry in order to assess the validity

Coherent structures and spectral energy transfer in turbulent plasma: A space-filter approach

Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, the formation and dissipation of thin current sheets, and stochastic heating. It is now understood that the presence of localized coherent structures enhances the dissipation channels and the kinetic features of the plasma. However, no formal way of quantifying the relationship between scale-to-scale energy transfer and the presence of spatial structures has been presented so far. In the Letter we quantify such a relationship analyzing the results of a two-dimensional high-resolution Hall magnetohydrodynamic simulation. In particular, we employ the technique of space filtering to derive a spectral energy flux term which defines, in any point of the computational domain, the signed flux of spectral energy across a given wave number. The characterization of coherent structures is performed by means of a traditional two-dimensional wavelet transformation. By studying the correlation between the spectral energy flux and the wavelet amplitude, we demonstrate the strong relationship between scale-to-scale transfer and coherent structures. Furthermore, by conditioning one quantity with respect to the other, we are able for the first time to quantify the inhomogeneity of the turbulence cascade induced by topological structures in the magnetic field. Taking into account the low space-filling factor of coherent structures (i.e., they cover a small portion of space), it emerges that 80% of the spectral energy transfer (both in the direct and inverse cascade directions) is localized in about 50% of space, and 50% of the energy transfer is localized in only 25% of space

Turbulence in Magnetic Reconnection Jets from Injection to Sub-Ion Scales

We investigate turbulence in magnetic reconnection jets in the Earth's magnetotail using data from the Magnetospheric Multiscale spacecraft. We show that fully developed turbulence is observed in many reconnection jets. The observed turbulence develops on the time scale of a few ion gyroperiods, resulting in intermittent multifractal energy cascade from the characteristic scale of the jet down to the ion scales. We show that at sub-ion scales, the fluctuations are close to mono-fractal and predominantly kinetic Alfv\'en waves. The observed energy transfer rate across the inertial range is the largest reported for space plasmas so far

To what extent can dynamical models describe statistical features of turbulent flows?

Statistical features of "bursty" behaviour in charged and neutral fluid turbulence, are compared to statistics of intermittent events in a GOY shell model, and avalanches in different models of Self Organized Criticality (SOC). It is found that inter-burst times show a power law distribution for turbulent samples and for the shell model, a property which is shared only in a particular case of the running sandpile model. The breakdown of self-similarity generated by isolated events observed in the turbulent samples, is well reproduced by the shell model, while it is absent in all SOC models considered. On this base, we conclude that SOC models are not adequate to mimic fluid turbulence, while the GOY shell model constitutes a better candidate to describe the gross features of turbulence.Comment: 14 pages, 4 figures, in press on Europhys. Lett. (may 2002